In a diagram there is a picture which is 16cm x 8cm surrounded by a border of width 4 cm forming a bigger rectangle. Are the two rectangles similar?

Here is the image. The quality is really bad but i hope its understanable
enter image source here

1 Answer
May 12, 2018

Your picture is fine! And no, they aren't similar.

Explanation:

The two rectangles will be similar if the ratio of their length to width are the same.

Let the width and length of the smaller rectangle be #w_s# and #l_s# respectively, and let #w_b# and #l_b# be the width and length of the larger rectangle (w and l for width and length, s and b for small and large, naturally).

#w_s=8"cm"#
#l_s=16"cm"#

So the ratio is #l_s/w_s=16/8#
#=2#

#w_b=w_s+8#
If its a border of 4cm all the way around, then this will be 8cm overall.
#w_b=8+8#
#=16"cm"#

#l_b=l_s+8#
#l_b=16+8#
#=24"cm"#

#l_b/w_b=24/16#
#=3/2#

#3/2!=2# therefore the two rectangles are not similar.